On small perturbations of Markov cyber threat models
Alexey Anatol'evich Magazev, V. F. Tsyrulnik · Journal of Physics Conference Series · 2021
Abstract In this work, we consider Markov chain-based stochastic modeling of cyber threats acting on computer systems. In the framework of this approach, computer systems are considered as systems with failures and recoveries by analogy with technical system models in reliability theory. Under the assumption that the cyber threats are independent random events, we derive the explicit analytic formulas for the state probabilities of the corresponding Markov chain and the mean time to security failure (MTSF). Then we investigate the case of dependent cyber threats and derive the approximate expressions for the state probabilities and MTSF within the framework of the first-order perturbation theory. As an illustration of our results, we consider a few simple examples.